Question

question
solve the system by substitution.
\\( x = 4y - 6 \\)
\\( -4x + 3y = -28 \\)

Explanation:

Step1: Substitute \( x = 4y - 6 \) into the second equation

We have the second equation \( -4x + 3y = -28 \). Substitute \( x \) with \( 4y - 6 \):
\( -4(4y - 6) + 3y = -28 \)

Step2: Simplify and solve for \( y \)

First, distribute the -4:
\( -16y + 24 + 3y = -28 \)
Combine like terms:
\( -13y + 24 = -28 \)
Subtract 24 from both sides:
\( -13y = -28 - 24 \)
\( -13y = -52 \)
Divide both sides by -13:
\( y = \frac{-52}{-13} = 4 \)

Step3: Substitute \( y = 4 \) back into \( x = 4y - 6 \) to find \( x \)

\( x = 4(4) - 6 \)
\( x = 16 - 6 = 10 \)

Answer:

The solution to the system is \( x = 10 \), \( y = 4 \) (or as an ordered pair \( (10, 4) \))